The only thing I know about MMR is that it influences your matchup with other players. I'm assuming its similar to the ELO system but I'm not exactly sure what that is either.
What is MMR? How is it calculated?
Match Making Rank (MMR) is a hidden Elo based rating system that is used for match making in game queues. Your actual MMR, and the exact means by which it is calculated, is hidden from players, so we can only speculate as to how it works based on observation.
MMR values correspond roughly to tier/division placing, but your MMR can be higher or lower than your actual tier/division position, based on your recent performance. For example, you could be ranked Silver 3, but with a streak of wins your MMR will increase and you will notice that the other players in your matches will be Silver 1 or Gold 5.
MMR is also used to determine how many league points are awarded/deducted for wins/losses, taking into account your own current MMR, and the average MMR of each team.
Basically, MMR is where the game thinks you should be placed, based on recent performance, and it will help accelerate you toward that position (up or down), if you perform consistently.
Also worth noting is that each player has a separate MMR value for each queue. Thus you can experiment with new champions and strategies in normal queues and have a lower win rate and a lower MMR than in ranked, where you might rely on tried and tested gameplay.
A couple of sites out there will give you an indicative number for your ranked MMR:
Important to note that both of these are just estimates, and are not official in any way.